Understanding MCMC Dynamics as Flows on the Wasserstein Space release_3am7mjbftzeshkmls6i4ibg4de

by Chang Liu, Jingwei Zhuo, Jun Zhu

Released as a article .

2019  

Abstract

It is known that the Langevin dynamics used in MCMC is the gradient flow of the KL divergence on the Wasserstein space, which helps convergence analysis and inspires recent particle-based variational inference methods (ParVIs). But no more MCMC dynamics is understood in this way. In this work, by developing novel concepts, we propose a theoretical framework that recognizes a general MCMC dynamics as the fiber-gradient Hamiltonian flow on the Wasserstein space of a fiber-Riemannian Poisson manifold. The "conservation + convergence" structure of the flow gives a clear picture on the behavior of general MCMC dynamics. The framework also enables ParVI simulation of MCMC dynamics, which enriches the ParVI family with more efficient dynamics, and also adapts ParVI advantages to MCMCs. We develop two ParVI methods for a particular MCMC dynamics and demonstrate the benefits in experiments.
In text/plain format

Archived Files and Locations

application/pdf  923.5 kB
file_bzrhr6v4pfa2lprnxiz4h2fivy
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2019-02-01
Version   v1
Language   en ?
arXiv  1902.00282v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 57eba8c7-4555-4fcb-9d51-466a49e41b2d
API URL: JSON